matrix representation
A matrix representation^{} of a group $G$ is a group homomorphism^{} between $G$ and $G{L}_{n}(\u2102)$, that is, a function
$$X:G\to G{L}_{n}(\u2102)$$ 
such that

•
$X(gh)=X(g)X(h)$,

•
$X(e)=I$
Notice that this definition is equivalent^{} to the group representation^{} definition when the vector space^{} $V$ is finite dimensional over $\u2102$. The parameter $n$ (or in the case of a group representation, the dimension^{} of $V$) is called the degree of the representation.
References
 1 Bruce E. Sagan. The Symmetric Group^{}: Representations, Combinatorial Algorithms^{} and Symmetric Functions. 2a Ed. 2000. Graduate Texts in Mathematics. Springer.
Title  matrix representation 

Canonical name  MatrixRepresentation 
Date of creation  20130322 14:53:56 
Last modified on  20130322 14:53:56 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  9 
Author  drini (3) 
Entry type  Definition 
Classification  msc 20C99 
Related topic  PermutationRepresentation 